# The switching effect of the side chain on quantum walks on triple graphs

## TL;DR

This paper studies how the length of a side chain affects quantum walk propagation on a triple graph, revealing a switching effect dependent on the side chain's parity and proposing experimental setups for observation.

## Contribution

It uncovers a parity-dependent switching effect in quantum walks on triple graphs influenced by side chain length and suggests experimental methods to observe this phenomenon.

## Key findings

- Switching effect occurs with odd side chain length under specific conditions.
- No switching effect when side chain length is even.
- Proposes experimental setups to observe the effect.

## Abstract

We consider a continuous-time quantum walk on a triple graph and investigate the influence of the side chain on the propagation in the main chain. Calculating the interchange of the probabilities between the two parts of the main chain, we find that a switching effect appears if there are odd number of points on the side chain when concrete conditions between the length of the main chain and the position of the side chain are satisfied. Whereas, such an effect does not occur if there are even number of points on the side chain. We also suggest two proposals for experiment to observe such an effect, which may be employed to design new type of switching device.